I'm always baffled by folks who assume self-driving cars would reduce traffic. No matter what, even if they are privately owned, truly self-driving vehicles could only increase traffic. If they can be dispatched without a human driver to pick up groceries or take-out, for example, there'll be a lot more trips. And sharing self-driving cars rather than owning them would surely be more likely to increase the number of cars on the road since they have to make a trip to pick you up and another one after they drop you off.
The rationale I have heard is that a single car could be used to make a multiple chained trips instead of multiple cars making multiple trips. This is the same idea behind ride sharing. I feel this breaks down with privately owned vehicles. I do see an increase in traffic in areas with expensive parking. Specifically I would sent my car to a cheaper lot and that would result in an additional trip. Even worse, that would be a zero occupancy trip.
I'm also pretty sure it will increase commutes and this applies even if self-driving isn't fully door to door. There are probably a lot of people who would hesitate to do an hour car commute today who would be a lot more open to a 60 or even 90 minute commute of something else is doing the driving.